5. Let F = -9zi+ (xe"² – 2xe²²)+ 12 k. Find ſg F .dÃ¸ and let S be the portionof the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (seefigure to the right), oriented upward.(a) Explain why the formula F Ã cannot be used to find the flux of F through the surface S. Please bespecific and use a complete sentence.

Given: F→=-9zi→+xexz-2xex2j→+12k→ The equation of the plain given is 2x+3z=6

Answered: = 6 that lies in the first oct riented…

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Step 1

Given:

$\vec{F} = - 9 z \vec{i} + (x e^{x z} - 2 x e^{x^{2}}) \vec{j} + 12 \vec{k}$

The equation of the plain given is $2 x + 3 z = 6$

Step 2

Since "S" is closed so divergence of "F" is given as follows,

Flux = $\int \int \int d i v F d v$

On applying the given equation in the above divergence,

$d i V F = \frac{\partial}{\partial x} (- 9 z) + \frac{\partial}{\partial y} (x e^{x z} - 2 x e^{x^{2}}) + \frac{\partial}{\partial z} (12)$

$d i V F = 0 + 0 + 0 = 0$

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